You can't burn to a writer that's shared as a drive over the network. Network burning software exists, but doesn't provide burn capabilities from any burning program you care to install on a remote system - it's more of a client/server system, where you set up a disc on your machine using the client, which is then passed to the server for burning.
Burning over the network itself would be fraught with difficulties because of the possible latency and lack of bandwidth. It's hard enough to burn files located somewhere on the network rather than on a local drive without caching (which many burning programs do automatically for network files).
If this is a regular need, why not put a CD-RW drive in your son's computer? It won't cost you much.